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I saw a popular demonstration of surface tension, where we have a tube and we blow 2 soap bubbles of unequal sizes then when we let the bubbles be connected to each other and not with the outer atmosphere then the smaller bubble blows the bigger bubble (because the pressure in the smaller bubble is more than the pressure in the bigger bubble), the smaller bubble becomes smaller.

But we know that the pressure inside a bubble is inversely proportional to the radius of the spherical surface. Hence, if air is flowing from the smaller to bigger bubble due to its pressure difference, the pressure inside the smaller bubble is becoming less, hence it should become bigger in size.

What is wrong in this argument?

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I think I have understood the issue in my argument. Pressure is related to the radius- not the size. Hence the smaller bubble is shrinking (due to decrease in volume of air) while its radius of curvature is increasing (due to decrease in pressure- again due to movement of air)

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